4 ms·

Yes, the PI really contains all information on the world, since it's an infinite non-periodic number. The only problem is that it also contains all noise on the

• sp332 16y ago
  Pi doesn't contain all the information in the world. It doesn't have the digits of the square root of 2, or the value of e, for example.
  • wtallis 16y ago
    If you assume that pi is a normal number (unproven, but likely) then it is almost certain (ie. probability 1) that the digits of e and the square root of 2 are subsequences of the digits of pi.
    • eru 16y ago
      What do you mean by subsequence? Don't normal numbers only have to contain every finite string often enough, not every infinite string?
      • wtallis 16y ago
        http://en.wikipedia.org/wiki/Normal_number http://en.wikipedia.org/wiki/Normal_number http://mathworld.wolfram.com/NormalNumber.html http://mathworld.wolfram.com/NormalNumber.html http://en.wikipedia.org/wiki/Subsequence http://en.wikipedia.org/wiki/Subsequence http://mathworld.wolfram.com/Subsequence.html http://mathworld.wolfram.com/Subsequence.html Does anybody want to explain why they downvoted a mathematical fact?
        • eru 16y ago
          To answer my questions (according to your links): Yes, normal numbers only have to satisfy conditions on finite strings. And subsequence means deleting some items out of a sequence.
          • JadeNB 16y ago
            Maybe this was your point, but it seems to me that, with these definition, wtallis's claim (http://news.ycombinator.com/item?id=1567549 http://news.ycombinator.com/item?id=1567549) is correct; indeed, one simply needs to find 1 at some point, then find 4 a little later, then 1 after that, then 4 again, then a 2, and so forth. The indices where one finds the desired digits become the indices of the claimed subsequence of digits of π.
            • eru 16y ago
              Indeed. And for the claim to be correct, even a much weaker condition than normality would suffice. E.g. a number like 0.123456789012345678901234567890[repeat] is definitely not normal, but contains all decimal subsequences.
  • wcoenen 16y ago
    But pi does contain the finite instruction sequences for programs that generate the digits of those numbers.
    • sp332 16y ago
      Well OK, the formula at this link will give you all the digits of pi: http://en.wikipedia.org/wiki/Numerical_approximations_of_%CF%80#BBP_formula_.28base_16.29 http://en.wikipedia.org/wiki/Numerical_approximations_of_%CF... The formula is clearly finite (on the order of 40 symbols), it does not contain "all the information in the world" and neither can any sequence it generates.
      • jerf 16y ago
        Information theory is a tricky beast. Pi contains no more information than it takes to express it, so in information theory terms it doesn't contain much information at all since it can be expressed very concisely. It so happens that pi + enough information to use pi as raw material to produce the desired information can output anything you like, which some people find amazing. But really, "anything + enough information to use 'anything' as raw material to produce the desired output" works equally well, too; pi isn't actually that special either. Also, the information needed to produce your desired output from pi is on average larger than the information in the desired output in the first place, which is why the "compress your things by referencing a digit number in pi" doesn't actually work. So, pi contains all the information in the world as long as you use more information to extract it from pi, in which case all you are really doing is expressing the original information in a particularly unpleasant encoding. But it sounds cool to say pi has all this information... "how can anything with an infinite number of normalized digits consist of only a handful of bits?" asks our feeble, mathematics-impaired human minds. (By the way, this is extended agreement with the post I'm replying to, not any implicit disagreement.)
• eru 16y ago
  > Yes, the PI really contains all information on the world, since it's an infinite non-periodic number. Non-periodicity doesn't suffice. A number that has increasing runs of zeroes divided by ones, is non-periodic, but doesn't contain everything. It's conjectured that Pi is a normal number [1], which would make your statement become true. [1] http://en.wikipedia.org/wiki/Normal_number http://en.wikipedia.org/wiki/Normal_number
  • eru 16y ago
    An even easier sequence is: The natural numbers. They also contain all imaginable digital sequences.